"Poroshenko also insisted that Ukrainian would remain the sole state language of the country, but promised 'new opportunities for the Russian language,' without giving specifics.

"He assumed power a day after meeting Russian President Vladimir Putin at D-Day commemoration ceremonies in France.

"Despite the outreach to Putin, Poroshenko said he will not accept Russia's annexation of Crimea.

" 'Crimea was, is and will be Ukrainian. There will be no trade-off,' Poroshenko said."

As always, a reminder: This whole conflict started after violent protests ended in the ouster of pro-Russian President Viktor Yanukovych. Seizing on the opportunity, Russia annexed Crimea, and the government in Kiev and some of its international partners — including the U.S. — worry that Russia is poised for further incursion into Ukrainian territory. Poroshenko is friendly with Europe and the United States.

As the BBC reports, Vice President Biden was present for Poroshenko's inauguration address.

The BBC adds that Poroshenko's speech was clearly intended for pro-revolution Ukrainians with hopes of joining the European Union.

Reuters reports that Russian President Vladimir Putin issued an order to "strengthen protection of the country's border with Ukraine to prevent people crossing illegally."

The wire service goes on to report that rebels in the east rejected Poroshenko's call.

"What they really want is one-sided disarmament and for us to surrender. That will never happen," top separatist official Fyodor Berezin told Reuters. "As long as Ukrainian troops are on our soil, I can see that all Poroshenko wants is subjugation."